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Speed of sound in methane under conditions of planetary interiors

Thomas G. White1,2,*, Hannah Poole2, Emma E. McBride3,4, Matthew Oliver1,2,5, Adrien Descamps3,4, Luke B. Fletcher3, W. Alex Angermeier1, Cameron H. Allen1, Karen Appel6 et al.

Florian P. Condamine7, Chandra B. Curry3,8, Francesco Dallari9, Stefan Funk10, Eric Galtier3, Eliseo J. Gamboa3, Maxence Gauthier3, Peter Graham11, Sebastian Goede6, Daniel Haden1, Jongjin B. Kim3, Hae Ja Lee3, Benjamin K. Ofori-Okai3, Scott Richardson11, Alex Rigby2, Christopher Schoenwaelder3, Peihao Sun9, Bastian L. Witte3, Thomas Tschentscher6, Ulf Zastrau6, Bob Nagler3, J. B. Hastings3, Giulio Monaco9, Dirk O. Gericke12, Siegfried H. Glenzer3, and Gianluca Gregori2

  • 1Department of Physics, University of Nevada, Reno, Nevada 89557, USA
  • 2Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 3SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
  • 4School of Mathematics and Physics, Queens University Belfast, University Road, Belfast BT7 1NN, United Kingdom
  • 5Central Laser Facility, STFC Rutherford-Appleton Laboratory, Chilton OX11 0QX, United Kingdom
  • 6European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
  • 7Extreme Light Infrastructure ERIC, ELI Beamlines Facility, Za Radnici 835, CZ-252 41 Dolni Brezany, Czech Republic
  • 8Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 1H9
  • 9Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Via F. Marzolo, 8, I-35131 Padova, Italy
  • 10Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen Centre for Astroparticle Physics, Nikolaus-Fiebiger-Str. 2, 91058 Erlangen, Germany
  • 11AWE, Aldermaston, Reading, Berkshire RG7 4PR, United Kingdom
  • 12Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

  • *Corresponding author: tgwhite@unr.edu

Phys. Rev. Research 6, L022029 – Published 2 May, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022029

Abstract

We present direct observations of acoustic waves in warm dense matter. We analyze wave-number- and energy-resolved x-ray spectra taken from warm dense methane created by laser heating a cryogenic liquid jet. X-ray diffraction and inelastic free-electron scattering yield sample conditions of 0.3±0.1 eV and 0.8±0.1 g/cm−3, corresponding to a pressure of ∼13 GPa. Inelastic x-ray scattering was used to observe the collective oscillations of the ions. With a highly improved energy resolution of ∼50 meV, we could clearly distinguish the Brillouin peaks from the quasielastic Rayleigh feature. Data at different wave numbers were utilized to derive a sound speed of 5.9±0.5 km/s, marking a high-temperature data point for methane and demonstrating consistency with Birch's law in this parameter regime.

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References (57)

  1. T. Guillot, Interiors of giant planets inside and outside the solar system, Science 286, 72 (1999).
  2. M. D. Knudson, M. P. Desjarlais, R. W. Lemke, T. R. Mattsson, M. French, N. Nettelmann, and R. Redmer, Probing the interiors of the ice giants: Shock compression of water to 700 GPa and 3.8 g/cm3, Phys. Rev. Lett. 108, 091102 (2012).
  3. D. Kraus, J. Vorberger, A. Pak, N. J. Hartley, L. B. Fletcher, S. Frydrych, E. Galtier, E. J. Gamboa, D. O. Gericke, S. H. Glenzer, E. Granados, M. J. MacDonald, A. J. MacKinnon, E. E. McBride, I. Nam, P. Neumayer, M. Roth, A. M. Saunders, A. K. Schuster, P. Sun et al., Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions, Nat. Astron. 1, 606 (2017).
  4. M. Ross, The ice layer in Uranus and Neptune—diamonds in the sky? Nature (London) 292, 435 (1981).
  5. U. R. Christensen, V. Holzwarth, and A. Reiners, Energy flux determines magnetic field strength of planets and stars, Nature (London) 457, 167 (2009).
  6. S. Ichimaru, Statistical Plasma Physics, Volume II: Condensed Plasmas, Frontiers in Physics (CRC Press, Boca Raton, FL, 2018),
  7. L. R. Benedetti, J. H. Nguyen, W. A. Caldwell, H. Liu, M. Kruger, and R. Jeanloz, Dissociation of CH4 at high pressures and temperatures: Diamond formation in giant planet interiors? Science 286, 100 (1999).
  8. D. Kraus, N. J. Hartley, S. Frydrych, A. K. Schuster, K. Rohatsch, M. Rödel, T. E. Cowan, S. Brown, E. Cunningham, T. van Driel, L. B. Fletcher, E. Galtier, E. J. Gamboa, A. Laso Garcia, D. O. Gericke, E. Granados, P. A. Heimann, H. J. Lee, M. J. MacDonald, A. J. MacKinnon et al., High-pressure chemistry of hydrocarbons relevant to planetary interiors and inertial confinement fusion, Phys. Plasmas 25, 056313 (2018).
  9. W. J. Nellis, D. C. Hamilton, and A. C. Mitchell, Electrical conductivities of methane, benzene, and polybutene shock compressed to 60 GPa (600 kbar), J. Chem. Phys. 115, 1015 (2001).
  10. B. L. Sherman, H. F. Wilson, D. Weeraratne, and B. Militzer, Ab initio simulations of hot dense methane during shock experiments, Phys. Rev. B 86, 224113 (2012).
  11. F. Ancilotto, G. L. Chiarotti, S. Scandolo, and E. Tosatti, Dissociation of methane into hydrocarbons at extreme (planetary) pressure and temperature, Science 275, 1288 (1997).
  12. N. Goldman, E. J. Reed, and L. E. Fried, Quantum mechanical corrections to simulated shock Hugoniot temperatures, J. Chem. Phys. 131, 204103 (2009).
  13. P. E. Grabowski, S. Hansen, M. Murillo, L. Stanton, F. Graziani, A. Zylstra, S. Baalrud, P. Arnault, A. Baczewski, L. Benedict, C. Blancard, O. Čertík, J. Clérouin, L. Collins, S. Copeland, A. Correa, J. Dai, J. Daligault, M. Desjarlais, M. Dharma-wardana et al., Review of the first charged-particle transport coefficient comparison workshop, High Energy Density Phys. 37, 100905 (2020).
  14. T. G. White, J. Dai, and D. Riley, Dynamic and transient processes in warm dense matter, Philos. Trans. R. Soc. London A 381, 20220223 (2023).
  15. N. Nettelmann, K. Wang, J. Fortney, S. Hamel, S. Yellamilli, M. Bethkenhagen, and R. Redmer, Uranus evolution models with simple thermal boundary layers, Icarus 275, 107 (2016).
  16. J. A. A'Hearn, M. M. Hedman, C. R. Mankovich, H. Aramona, and M. S. Marley, Ring seismology of the ice giants uranus and neptune, Planet. Sci. J. 3, 194 (2022).
  17. D. Ikuta, E. Ohtani, H. Fukui, T. Sakai, D. Ishikawa, and A. Q. R. Baron, Sound velocity of hexagonal close-packed iron to the Earth's inner core pressure, Nat. Commun. 13, 7211 (2022).
  18. P. W. Bridgman, The thermal conductivity of liquids under pressure, Proc. Am. Acad. Arts Sci. 59, 141 (1923).
  19. S. A. Khrapak, Bridgman formula for the thermal conductivity of atomic and molecular liquids, J. Mol. Liq. 381, 121786 (2023).
  20. F. Birch, Density and composition of mantle and core, J. Geophys. Res. 69, 4377 (1964).
  21. D. W. Meyer, W.-P. Hsieh, H. Hsu, C.-Y. Kuo, and J.-F. Lin, Thermal conductivity and compressional velocity of methane at high pressure: Insights into thermal transport properties of icy planet interiors, J. Geophys. Res.: Planets 127, e2021JE007059 (2022).
  22. T. Sakamaki, E. Ohtani, H. Fukui, S. Kamada, S. Takahashi, T. Sakairi, A. Takahata, T. Sakai, S. Tsutsui, D. Ishikawa, R. Shiraishi, Y. Seto, T. Tsuchiya, and A. Q. R. Baron, Constraints on Earth's inner core composition inferred from measurements of the sound velocity of hcp-iron in extreme conditions, Sci. Adv. 2, e1500802 (2016).
  23. J. Bouchet, F. Bottin, D. Antonangeli, and G. Morard, Sound velocities and thermodynamical properties of hcp iron at high pressure and temperature, J. Phys.: Condens. Matter 34, 344002 (2022).
  24. S. H. Glenzer, G. Gregori, R. W. Lee, F. J. Rogers, S. W. Pollaine, and O. L. Landen, Demonstration of spectrally resolved x-ray scattering in dense plasmas, Phys. Rev. Lett. 90, 175002 (2003).
  25. S. H. Glenzer, O. L. Landen, P. Neumayer, R. W. Lee, K. Widmann, S. W. Pollaine, R. J. Wallace, G. Gregori, A. Höll, T. Bornath, R. Thiele, V. Schwarz, W.-D. Kraeft, and R. Redmer, Observations of plasmons in warm dense matter, Phys. Rev. Lett. 98, 065002 (2007).
  26. T. Ma, T. Döppner, R. W. Falcone, L. Fletcher, C. Fortmann, D. O. Gericke, O. L. Landen, H. J. Lee, A. Pak, J. Vorberger, K. Wünsch, and S. H. Glenzer, X-ray scattering measurements of strong ion-ion correlations in shock-compressed aluminum, Phys. Rev. Lett. 110, 065001 (2013).
  27. L. B. Fletcher, H. J. Lee, T. Döppner, E. Galtier, B. Nagler, P. Heimann, C. Fortmann, S. LePape, T. Ma, M. Millot, A. Pak, D. Turnbull, D. A. Chapman, D. O. Gericke, J. Vorberger, T. White, G. Gregori, M. Wei, B. Barbrel, R. W. Falcone et al., Ultrabright x-ray laser scattering for dynamic warm dense matter physics, Nat. Photonics 9, 274 (2015).
  28. T. Döppner, M. Bethkenhagen, D. Kraus, P. Neumayer, D. A. Chapman, B. Bachmann, R. A. Baggott, M. P. Böhme, L. Divol, R. W. Falcone, L. B. Fletcher, O. L. Landen, M. J. MacDonald, A. M. Saunders, M. Schörner, P. A. Sterne, J. Vorberger, B. B. L. Witte, A. Yi, R. Redmer et al., Observing the onset of pressure-driven K-shell delocalization, Nature (London) 618, 270 (2023).
  29. E. E. McBride, T. G. White, A. Descamps, L. B. Fletcher, K. Appel, F. P. Condamine, C. B. Curry, F. Dallari, S. Funk, E. Galtier, M. Gauthier, S. Goede, J. B. Kim, H. J. Lee, B. K. Ofori-Okai, M. Oliver, A. Rigby, C. Schoenwaelder, P. Sun, Th. Tschentscher et al., Setup for meV-resolution inelastic x-ray scattering measurements and x-ray diffraction at the Matter in Extreme Conditions endstation at the Linac Coherent Light Source, Rev. Sci. Instrum. 89, 10F104 (2018).
  30. A. Descamps, B. K. Ofori-Okai, J. K. Baldwin, Z. Chen, L. B. Fletcher, S. H. Glenzer, N. J. Hartley, J. B. Hasting, D. Khaghani, M. Mo, B. Nagler, V. Recoules, R. Redmer, M. Schörner, P. Sun, Y. Q. Wang, T. G. White, and E. E. McBride, Towards performing high-resolution inelastic x-ray scattering measurements at hard x-ray free-electron lasers coupled with energetic laser drivers, J. Synchrotron Radiat. 29, 931 (2022).
  31. R. Verbeni, M. Kocsis, S. Huotari, M. Krisch, G. Monaco, F. Sette, and G. Vanko, Advances in crystal analyzers for inelastic x-ray scattering, J. Phys. Chem. Solids 66, 2299 (2005).
  32. G. Blaj, P. Caragiulo, G. Carini, S. Carron, A. Dragone, D. Freytag, G. Haller, P. Hart, J. Hasi, R. Herbst, S. Herrmann, C. Kenney, B. Markovic, K. Nishimura, S. Osier, J. Pines, B. Reese, J. Segal, A. Tomada, and M. Weaver, X-ray detectors at the Linac coherent light source, J. Synchrotron Radiat. 22, 577 (2015).
  33. J. B. Kim, C. Schoenwaelder, and S. H. Glenzer, Development and characterization of liquid argon and methane microjets for high-rep-rate laser-plasma experiments, Rev. Sci. Instrum. 89, 10K105 (2018).
  34. C. B. Curry, C. Schoenwaelder, S. Goede, J. B. Kim, M. Rehwald, F. Treffert, K. Zeil, S. H. Glenzer, M. Gauthier, C. B. Curry, J. B. Kim, and S. H. Glenzer, Cryogenic liquid jets for high repetition rate discovery science, J. Vis. Exp., e61130 (2020).
  35. C. Prescher and V. B. Prakapenka, DIOPTAS: A program for reduction of two-dimensional x-ray diffraction data and data exploration, High Press. Res. 35, 223 (2015).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022029 for details of the MCMS fitting procedure, detector calibration, and additional collected spectra.
  37. J. A. Bearden, X-ray wavelengths, Rev. Mod. Phys. 39, 78 (1967).
  38. D. Pines and D. Bohm, A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions, Phys. Rev. 85, 338 (1952).
  39. S. H. Glenzer and R. Redmer, X-ray Thomson scattering in high energy density plasmas, Rev. Mod. Phys. 81, 1625 (2009).
  40. G. Gregori, S. H. Glenzer, F. J. Rogers, S. M. Pollaine, O. L. Landen, C. Blancard, G. Faussurier, P. Renaudin, S. Kuhlbrodt, and R. Redmer, Electronic structure measurements of dense plasmas, Phys. Plasmas 11, 2754 (2004).
  41. G. Gregori, A. Ravasio, A. Höll, S. Glenzer, and S. Rose, Derivation of the static structure factor in strongly coupled non-equilibrium plasmas for x-ray scattering studies, High Energy Density Phys. 3, 99 (2007).
  42. G. Gregori, S. H. Glenzer, W. Rozmus, R. W. Lee, and O. L. Landen, Theoretical model of x-ray scattering as a dense matter probe, Phys. Rev. E 67, 026412 (2003).
  43. T. Döppner, A. L. Kritcher, D. Kraus, S. H. Glenzer, B. L. Bachmann, D. Chapman, G. W. Collins, R. W. Falcone, J. Hawreliak, O. L. Landen, H. J. Lee, S. L. Pape, T. Ma, P. Neumayer, R. Redmer, and D. C. Swift, X-ray Thomson scattering as a temperature probe for Gbar shock experiments, J. Phys.: Conf. Ser. 500, 192019 (2014).
  44. M. F. Kasim, T. P. Galligan, J. Topp-Mugglestone, G. Gregori, and S. M. Vinko, Inverse problem instabilities in large-scale modeling of matter in extreme conditions, Phys. Plasmas 26, 112706 (2019).
  45. H. Poole, D. Cao, R. Epstein, I. Golovkin, T. Walton, S. X. Hu, M. Kasim, S. M. Vinko, J. R. Rygg, V. N. Goncharov, G. Gregori, and S. P. Regan, A case study of using x-ray Thomson scattering to diagnose the in-flight plasma conditions of DT cryogenic implosions, Phys. Plasmas 29, 072703 (2022).
  46. J. MacFarlane, I. Golovkin, and P. Woodruff, HELIOS-CR—A 1-D radiation-magnetohydrodynamics code with inline atomic kinetics modeling, J. Quant. Spectrosc. Radiat. Transfer 99, 381 (2006).
  47. H. Hirai, K. Konagai, T. Kawamura, Y. Yamamoto, and T. Yagi, Polymerization and diamond formation from melting methane and their implications in ice layer of giant planets, Phys. Earth Planet. Inter. 174, 242 (2009).
  48. A. Habenschuss, E. Johnson, and A. H. Narten, X-ray diffraction study and models of liquid methane at 92 K, J. Chem. Phys. 74, 5234 (1981).
  49. R. Helled, N. Nettelmann, and T. Guillot, Uranus and Neptune: Origin, evolution and internal structure, Space Sci. Rev. 216, 38 (2020).
  50. A. Vazan and R. Helled, Explaining the low luminosity of Uranus: A self-consistent thermal and structural evolution, Astron. Astrophys. 633, A50 (2020).
  51. A. Descamps, B. K. Ofori-Okai, K. Appel, V. Cerantola, A. Comley, J. H. Eggert, L. B. Fletcher, D. O. Gericke, S. Göde, O. Humphries, O. Karnbach, A. Lazicki, R. Loetzsch, D. McGonegle, C. A. J. Palmer, C. Plueckthun, T. R. Preston, R. Redmer, D. G. Senesky, C. Strohm et al., An approach for the measurement of the bulk temperature of single crystal diamond using an x-ray free electron laser, Sci. Rep. 10, 14564 (2020).
  52. J. Boon and S. Yip, Molecular Hydrodynamics, Dover Books on Physics (Dover, New York, 1991).
  53. R. Schmidt, B. J. B. Crowley, J. Mithen, and G. Gregori, Quantum hydrodynamics of strongly coupled electron fluids, Phys. Rev. E 85, 046408 (2012).
  54. J. P. Mithen, J. Daligault, and G. Gregori, Extent of validity of the hydrodynamic description of ions in dense plasmas, Phys. Rev. E 83, 015401(R) (2011).
  55. J. Vorberger, Z. Donko, I. M. Tkachenko, and D. O. Gericke, Dynamic ion structure factor of warm dense matter, Phys. Rev. Lett. 109, 225001 (2012).
  56. T. Guillot, Uranus and Neptune are key to understand planets with hydrogen atmospheres, Exp. Astron. 54, 1027 (2022).
  57. S. Markham and D. Stevenson, Excitation mechanisms for Jovian seismic modes, Icarus 306, 200 (2018).

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